Expectation Value of a component of Orbital Angular Momentum

[Josh158]

Homework Statement

given a certain state |ψ> that is an eigenstate of L^2 and Lz
Calculate <Lx^2> and <Lx>

Homework Equations

L^2|ψ> = l(l+1)h^2
Lz|ψ> = mh|ψ>
Lx = YPz - ZPy

The Attempt at a Solution

<Lx^2> = (1/2)(h^2)[l(l+1)-(m1)^2]

for Lx i got
<Lx> = ∫ψ(YPz-ZPy)ψ dx

 

[vela]

Try writing L_x in terms of the raising and lowering operators.